Geometry and scaling of tangled vortex lines in three-dimensional random wave fields

The short- and long-scale behaviour of tangled wave vortices (nodal lines) in random three-dimensional (3D) wave fields is studied via computer experiment. The zero lines are tracked in numerical simulations of periodic superpositions of 3D complex plane waves. The probability distribution of local geometric quantities such as curvature and torsion are compared to previous analytical and new Monte Carlo results from the isotropic Gaussian random wave model. We further examine the scaling and self-similarity of tangled wave vortex lines individually and in the bulk, drawing comparisons with other physical systems of tangled filaments.